Least square procedures to improve the results of the three-parameter sine fitting algorithm

The paper presents two approaches to improve the three parameter sine fitting algorithm and attain accurate estimates of the parameters of a sinusoidal signal corrupted by noise. As the four parameter sine fitting algorithm, which is usually adopted to improve the estimates of the three parameter algorithm, in theory, the proposed ones can be inserted into iterative schemes and repeated until a target precision is gained. Anyway, the use of the proposed algorithms is particularly suggested for those applications in which the results must be gained in very short times, which are in contrast to long iterative procedures. In these cases, when a single run of the algorithms has to offer the required improvement, the proposed ones are valid alternatives with respect to the four parameter algorithm, sharing with it almost comparable accuracy.